Where are the stitches located? And how extensive are they? Much will probably depend on the type of injury.
A little less than three years ago, I had (about sixteen) stitches running up my neck around and the side of my skull. I was knocked out when the surgeons put them in, so I don't remember that part. While they were in, I remember that area feeling tight and sore, but it wasn't outright painful (although I was originally given some pretty heavy-duty painkillers). I don't recall the stitches themselves being a big deal or very eventful in themselves. You just need to watch for redness or swelling, which could be sign of an infection.
One thing that may interest you is that they use a thick, slick plastic type black thread. It looks very harsh around the wound and against your skin. In all my experience with stitches they always create and knot off each stitch individually. It's not sewn up like you would sew cloth, in a continuous stitch. And they numb the area beforehand, so it just feels more like a tugging when they put the stitches in, but not actual pain. I have kids and have seen stitches quite a few times, and the process and material has always been the same.
Taking the stitches out was really quick and simple. The wound doesn't stick to the thread. Strangely enough, the stitches look a bit loose as they heal and aren't tight to the skin. If anything, there's a very brief, mild tickle as they cut the thread and pull it out. It's not painful and no painkiller is needed for that part.